Difference between revisions of "Manuals/calci/IMPOWER"

Revision as of 23:42, 19 December 2013

IMPOWER(z,n)

This function gives the value of powers of complex number.
DeMoivre's Theorem is a generalized formula to compute powers of a complex number in it's polar form.
i'is the imaginary unit, $i={\sqrt {-1}}$
Then the power of a complex number is defined by $(z)^{n}=(x+iy)^{n}=r^{n}*e^{in\theta }=r^{n}(cosn\theta +isinn\theta )$ where $r={\sqrt {x^{2}+y^{2}}}$ . and $\theta =tan^{-}1(y/x)$ , Failed to parse (syntax error): {\displaystyle \theta∈(-\pi,\pi]} .
This formula is called DeMoivre's theorem of complex numbers.
We can use COMPLEX function to convert real and imaginary number in to a complex number.
In IMPOWER(z,n), $n$ can be integer, fractional or negative.
If $n$ is non-numeric, function will return error value.

@@ Line 7: / Line 7: @@
 *DeMoivre's Theorem is a generalized formula to compute powers of a complex number in it's polar form.
 *i'is the imaginary unit,  <math>i=\sqrt{-1}</math>
-*Then the power of a complex number is defined by <math>(z)^n=(x+iy)^n=r^n*e^{inθ}=r^n(cosnθ+isinnθ)</math> where  <math>r=\sqrt{x^2+y^2}</math>. and  <math>θ=tan^-1(y/x)</math>, θ∈(-Pi(),Pi()].
+*Then the power of a complex number is defined by <math>(z)^n=(x+iy)^n=r^n*e^{in\theta}=r^n(cosn\theta+isinn\theta)</math> where <math>r=\sqrt{x^2+y^2}</math>. and  <math>\theta=tan^-1(y/x)</math>, <math>\theta∈(-\pi,\pi]</math>.
 *This formula is called DeMoivre's theorem of complex numbers.
-*We can use [[Manuals/calci/COMPLEX| COMPLEX]] function to convert   real and imaginary number in to a complex number.
+*We can use [[Manuals/calci/COMPLEX| COMPLEX]] function to convert real and imaginary number in to a complex number.
-*In IMPOWER(z,n), n can be integer, fractional or negative.
+*In IMPOWER(z,n), <math>n</math> can be integer, fractional or negative.
-*suppose n is nonnumeric , this function will returns the error value.
+*If <math>n</math> is non-numeric, function will return error value.
 ==Examples==